Population coding in the cerebellum: a machine learning perspective

The olivary input to the cerebellum dissociates sensory events from movement plans

Neurons in the inferior olive are thought to anatomically organize the Purkinje cells (P-cells) of the cerebellum into computational modules, but what is computed by each module? Here, we designed a saccade task in marmosets that dissociated sensory events from motor events and then recorded the complex and simple spikes of hundreds of P-cells. We found that when a visual target was presented at a random location, the olive reported the direction of that sensory event to one group of P-cells, but not to a second group. However, just before movement onset, it reported the direction of the planned movement to both groups, even if that movement was not toward the target. At the end of the movement if the subject experienced an error but chose to withhold the corrective movement, only the first group received information about the sensory prediction error. We organized the P-cells based on the information content of their olivary input and found that in the group that received sensory information, the simple spikes were suppressed during fixation, then produced a burst before saccade onset in a direction consistent with assisting the movement. In the second group, the simple spikes were not suppressed during fixation but burst near saccade deceleration in a direction consistent with stopping the movement. Thus, the olive differentiated the P-cells based on whether they would receive sensory or motor information, and this defined their contributions to control of movements as well as holding still.

Mesoscale simulations predict the role of synergistic cerebellar plasticity during classical eyeblink conditioning

According to the motor learning theory by Albus and Ito, synaptic depression at the parallel fibre to Purkinje cells synapse (pf-PC) is the main substrate responsible for learning sensorimotor contingencies under climbing fibre control. However, recent experimental evidence challenges this relatively monopolistic view of cerebellar learning. Bidirectional plasticity appears crucial for learning, in which different microzones can undergo opposite changes of synaptic strength (e.g. downbound microzones-more likely depression, upbound microzones-more likely potentiation), and multiple forms of plasticity have been identified, distributed over different cerebellar circuit synapses. Here, we have simulated classical eyeblink conditioning (CEBC) using an advanced spiking cerebellar model embedding downbound and upbound modules that are subject to multiple plasticity rules. Simulations indicate that synaptic plasticity regulates the cascade of precise spiking patterns spreading throughout the cerebellar cortex and cerebellar nuclei. CEBC was supported by plasticity at the pf-PC synapses as well as at the synapses of the molecular layer interneurons (MLIs), but only the combined switch-off of both sites of plasticity compromised learning significantly. By differentially engaging climbing fibre information and related forms of synaptic plasticity, both microzones contributed to generate a well-timed conditioned response, but it was the downbound module that played the major role in this process. The outcomes of our simulations closely align with the behavioural and electrophysiological phenotypes of mutant mice suffering from cell-specific mutations that affect processing of their PC and/or MLI synapses. Our data highlight that a synergy of bidirectional plasticity rules distributed across the cerebellum can facilitate finetuning of adaptive associative behaviours at a high spatiotemporal resolution.

Emergence of syntax and word prediction in an artificial neural circuit of the cerebellum

The cerebellum, interconnected with the cerebral neocortex, plays a vital role in human-characteristic cognition such as language processing, however, knowledge about the underlying circuit computation of the cerebellum remains very limited. To gain a better understanding of the computation underlying cerebellar language processing, we developed a biologically constrained cerebellar artificial neural network (cANN) model, which implements the recently identified cerebello-cerebellar recurrent pathway. We found that while cANN acquires prediction of future words, another function of syntactic recognition emerges in the middle layer of the prediction circuit. The recurrent pathway of the cANN was essential for the two language functions, whereas cANN variants with further biological constraints preserved these functions. Considering the uniform structure of cerebellar circuitry across all functional domains, the single-circuit computation, which is the common basis of the two language functions, can be generalized to fundamental cerebellar functions of prediction and grammar-like rule extraction from sequences, that underpin a wide range of cerebellar motor and cognitive functions. This is a pioneering study to understand the circuit computation of human-characteristic cognition using biologically-constrained ANNs.

Rate versus synchrony codes for cerebellar control of motor behavior

Information transmission between neural populations could occur through either coordinated changes in firing rates or the precise transmission of spike timing. We investigate the code for information transmission from a part of the cerebellar cortex that is crucial for the accurate execution of a quantifiable motor behavior. Simultaneous recordings from Purkinje cell pairs in the cerebellum of rhesus macaques reveal how these cells coordinate their activity to drive smooth pursuit eye movements. Purkinje cells show millisecond-scale coordination of spikes (synchrony), but the level of synchrony is small and insufficient to impact the firing of downstream vestibular nucleus neurons. Analysis of previous metrics that purported to reveal Purkinje cell synchrony demonstrates that these metrics conflate changes in firing rate and neuron-neuron covariance. We conclude that the output of the cerebellar cortex uses primarily a rate rather than a synchrony code to drive the activity of downstream neurons and thus control motor behavior.

The study of plasticity has always been about gradients

The experimental study of learning and plasticity has always been driven by an implicit question: how can physiological changes be adaptive and improve performance? For example, in Hebbian plasticity only synapses from presynaptic neurons that were active are changed, avoiding useless changes. Similarly, in dopamine-gated learning synapse changes depend on reward or lack thereof and do not change when everything is predictable. Within machine learning we can make the question of which changes are adaptive concrete: performance improves when changes correlate with the gradient of an objective function quantifying performance. This result is general for any system that improves through small changes. As such, physiology has always implicitly been seeking mechanisms that allow the brain to approximate gradients. Coming from this perspective we review the existing literature on plasticity-related mechanisms, and we show how these mechanisms relate to gradient estimation. We argue that gradients are a unifying idea to explain the many facets of neuronal plasticity.

Mechanisms of sensorimotor adaptation in a hierarchical state feedback control model of speech

Upon perceiving sensory errors during movements, the human sensorimotor system updates future movements to compensate for the errors, a phenomenon called sensorimotor adaptation. One component of this adaptation is thought to be driven by sensory prediction errors-discrepancies between predicted and actual sensory feedback. However, the mechanisms by which prediction errors drive adaptation remain unclear. Here, auditory prediction error-based mechanisms involved in speech auditory-motor adaptation were examined via the feedback aware control of tasks in speech (FACTS) model. Consistent with theoretical perspectives in both non-speech and speech motor control, the hierarchical architecture of FACTS relies on both the higher-level task (vocal tract constrictions) as well as lower-level articulatory state representations. Importantly, FACTS also computes sensory prediction errors as a part of its state feedback control mechanism, a well-established framework in the field of motor control. We explored potential adaptation mechanisms and found that adaptive behavior was present only when prediction errors updated the articulatory-to-task state transformation. In contrast, designs in which prediction errors updated forward sensory prediction models alone did not generate adaptation. Thus, FACTS demonstrated that 1) prediction errors can drive adaptation through task-level updates, and 2) adaptation is likely driven by updates to task-level control rather than (only) to forward predictive models. Additionally, simulating adaptation with FACTS generated a number of important hypotheses regarding previously reported phenomena such as identifying the source(s) of incomplete adaptation and driving factor(s) for changes in the second formant frequency during adaptation to the first formant perturbation. The proposed model design paves the way for a hierarchical state feedback control framework to be examined in the context of sensorimotor adaptation in both speech and non-speech effector systems.

Rate versus synchrony codes for cerebellar control of motor behavior

Control of movement requires the coordination of multiple brain areas, each containing populations of neurons that receive inputs, process these inputs via recurrent dynamics, and then relay the processed information to downstream populations. Information transmission between neural populations could occur through either coordinated changes in firing rates or the precise transmission of spike timing. We investigate the nature of the code for transmission of signals to downstream areas from a part of the cerebellar cortex that is crucial for the accurate execution of a quantifiable motor behavior. Simultaneous recordings from Purkinje cell pairs in the cerebellar flocculus of rhesus macaques revealed how these cells coordinate their activity to drive smooth pursuit eye movements. Purkinje cells show millisecond-scale coordination of spikes (synchrony), but the level of synchrony is small and likely insufficient to impact the firing of downstream neurons in the vestibular nucleus. Further, analysis of previous metrics for assaying Purkinje cell synchrony demonstrates that these metrics conflate changes in firing rate and neuron-neuron covariance. We conclude that the output of the cerebellar cortex uses primarily a rate code rather than synchrony code to drive activity of downstream neurons and thus control motor behavior.

IMPACT STATEMENT

Information transmission in the brain can occur via changes in firing rate or via the precise timing of spikes. Simultaneous recordings from pairs of Purkinje cells in the floccular complex reveals that information transmission out of the cerebellar cortex relies almost exclusively on changes in firing rates rather than millisecond-scale coordination of spike timing across the Purkinje cell population.

Dual STDP processes at Purkinje cells contribute to distinct improvements in accuracy and speed of saccadic eye movements

Saccadic eye-movements play a crucial role in visuo-motor control by allowing rapid foveation onto new targets. However, the neural processes governing saccades adaptation are not fully understood. Saccades, due to the short-time of execution (20-100 ms) and the absence of sensory information for online feedback control, must be controlled in a ballistic manner. Incomplete measurements of the movement trajectory, such as the visual endpoint error, are supposedly used to form internal predictions about the movement kinematics resulting in predictive control. In order to characterize the synaptic and neural circuit mechanisms underlying predictive saccadic control, we have reconstructed the saccadic system in a digital controller embedding a spiking neural network of the cerebellum with spike timing-dependent plasticity (STDP) rules driving parallel fiber-Purkinje cell long-term potentiation and depression (LTP and LTD). This model implements a control policy based on a dual plasticity mechanism, resulting in the identification of the roles of LTP and LTD in regulating the overall quality of saccade kinematics: it turns out that LTD increases the accuracy by decreasing visual error and LTP increases the peak speed. The control policy also required cerebellar PCs to be divided into two subpopulations, characterized by burst or pause responses. To our knowledge, this is the first model that explains in mechanistic terms the visual error and peak speed regulation of ballistic eye movements in forward mode exploiting spike-timing to regulate firing in different populations of the neuronal network. This elementary model of saccades could be extended and applied to other more complex cases in which single jerks are concatenated to compose articulated and coordinated movements.

Synchronous spiking of cerebellar Purkinje cells during control of movements

SignificanceThe information that one region of the brain transmits to another is usually viewed through the lens of firing rates. However, if the output neurons could vary the timing of their spikes, then, through synchronization, they would spotlight information that may be critical for control of behavior. Here we report that, in the cerebellum, Purkinje cell populations that share a preference for error convey, to the nucleus, when to decelerate the movement, by reducing their firing rates and temporally synchronizing the remaining spikes.

The cost of correcting for error during sensorimotor adaptation

Learning from error is often a slow process. In machine learning, the learning rate depends on a loss function that specifies a cost for error. Here, we hypothesized that during motor learning, error carries an implicit cost for the brain because the act of correcting for error consumes time and energy. Thus, if this implicit cost could be increased, it may robustly alter how the brain learns from error. To vary the implicit cost of error, we designed a task that combined saccade adaptation with motion discrimination: movement errors resulted in corrective saccades, but those corrections took time away from acquiring information in the discrimination task. We then modulated error cost using coherence of the discrimination task and found that when error cost was large, pupil diameter increased and the brain learned more from error. However, when error cost was small, the pupil constricted and the brain learned less from the same error. Thus, during sensorimotor adaptation, the act of correcting for error carries an implicit cost for the brain. Modulating this cost affects how much the brain learns from error.

Diverse inhibitory projections from the cerebellar interposed nucleus

The cerebellum consists of parallel circuit modules that contribute to diverse behaviors, spanning motor to cognitive. Recent work employing cell-type-specific tracing has identified circumscribed output channels of the cerebellar nuclei (CbN) that could confer tight functional specificity. These studies have largely focused on excitatory projections of the CbN, however, leaving open the question of whether inhibitory neurons also constitute multiple output modules. We mapped output and input patterns to intersectionally restricted cell types of the interposed and adjacent interstitial nuclei in mice. In contrast to the widespread assumption of primarily excitatory outputs and restricted inferior olive-targeting inhibitory output, we found that inhibitory neurons from this region ramified widely within the brainstem, targeting both motor- and sensory-related nuclei, distinct from excitatory output targets. Despite differences in output targeting, monosynaptic rabies tracing revealed largely shared afferents to both cell classes. We discuss the potential novel functional roles for inhibitory outputs in the context of cerebellar theory.

Adaptive control of movement deceleration during saccades

As you read this text, your eyes make saccades that guide your fovea from one word to the next. Accuracy of these movements require the brain to monitor and learn from visual errors. A current model suggests that learning is supported by two different adaptive processes, one fast (high error sensitivity, low retention), and the other slow (low error sensitivity, high retention). Here, we searched for signatures of these hypothesized processes and found that following experience of a visual error, there was an adaptive change in the motor commands of the subsequent saccade. Surprisingly, this adaptation was not uniformly expressed throughout the movement. Rather, after experience of a single error, the adaptive response in the subsequent trial was limited to the deceleration period. After repeated exposure to the same error, the acceleration period commands also adapted, and exhibited resistance to forgetting during set-breaks. In contrast, the deceleration period commands adapted more rapidly, but suffered from poor retention during these same breaks. State-space models suggested that acceleration and deceleration periods were supported by a shared adaptive state which re-aimed the saccade, as well as two separate processes which resembled a two-state model: one that learned slowly and contributed primarily via acceleration period commands, and another that learned rapidly but contributed primarily via deceleration period commands.

Part I: The Complex Spikes as One of the Cerebellar Secrets

The olivocerebellar tract has unique morphological, physiological, and developmental properties. Olivocerebellar axons are the source of multiple climbing fibers (CFs). The synapse between CFs and the Purkinje neuron is one of the most powerful excitatory in the central nervous system. Complex spikes are composed of an initial large amplitude spike followed by spikelets. The spatiotemporal patterns of complex/simple spikes complement the rate coding to enhance the accuracy of motor and cognitive processing, and to improve predictions related to internal models. Understanding the role of complex spikes is essential in clarifying how the cerebellar cortex contributes to learning, motor control, cognitive tasks, and the processing of emotions. This Cerebellar Classic is devoted to the pioneering work of Eccles, Llinás, and Sasaki on complex spikes using intracellular recordings from Purkinje neurons.